Question

Could someone help please?

The Sales S (in thousands of units) of a cleaning solution after X hundred dollars is spent on advertising are given:
S = 10(1 - e^(kx))
Now when $325 is spent on advertising 2300 units are sold.

(a)Complete by solving for k. (Round your answer to 4 decimal places)
k = _______

(b) What number of units that will be sold if advertising is raised up to $425
_______ Units.

Answer 1

`2.3=10(1-e^(3.25k)))\\ 2.3=10-10e^(3.25k)\\ 10e^(3.25k)=7.7\\ e^(3.25k)=0.77\\ 3.25k=\ln 0.77\\ k=(\ln 0.77)/(3.25)\\ k\approx-0.0804`


`S=10(1-e^{(\ln 0.77)/(3.25)\cdot4.25})\\`

Calculating this is a pain in the ***, but as a result you get approximately 2.8949 which in thousands of units is 2894 (rounded down since you can't have a fraction of a unit).